Evaluation of the equivalent damping ratio of seismically retrofitted historic churches with dissipative roof structures

The paper is focused on the evaluation of the equivalent damping ratio (EDR) given by wood-based dissipative roof-diaphragm in the nave transversal response of historic churches under seismic actions. In the refurbishment of this type of building, EDR represents a key parameter in designing the optimum roof structure and achieving the maximum energy dissipation, reducing the lateral displacement of the top of masonry walls and containing the in-plane shear forces acting on the roof and the head walls. First, an equivalent frame model of the church structure is implemented including inelastic rotational hinges for the nonlinear properties of masonry walls and inelastic shear hinges for the nonlinear behavior of the roof steel connections. The transversal response of the nave is described as a function of a hysteretic variable, which depends on the ratio between the yield load of the masonry walls and roof connections. By changing the value of the hysteretic variable, possible configurations of the roof-diaphragms are designed and analyzed, leading to the selection of the optimal one capable of properly limiting the top displacements and the in-plane shear actions. Under these conditions, the corresponding EDR values are evaluated according to the coefficient method of FEMA 345 and the equivalent linearization technique of ATC-40, by means of nonlinear pushover analyses (PO). Moreover, for comparison, EDR values are also evaluated from the results of nonlinear time history (TH) analyses of the retrofitted configuration of the church under a set of seven spectrum-compatible accelerograms. The TH approach considers the dissipative contribution of the inelastic hinges of the walls and roof connections by evaluating the plastic and strain energies along the cycles, for each one of the considered earthquakes. In the EDR evaluations according to FEMA 345, ATC-40, and TH method, two different hysteretic behaviors of the roof’s steel connections are adopted: skeleton curves with stiffness degradation and trilinear model with strength and stiffness degradation.